A064771 Let S(n) = set of divisors of n, excluding n; sequence gives n such that there is a unique subset of S(n) that sums to n.

6, 20, 28, 78, 88, 102, 104, 114, 138, 174, 186, 222, 246, 258, 272, 282, 304, 318, 354, 366, 368, 402, 426, 438, 464, 474, 490, 496, 498, 534, 572, 582, 606, 618, 642, 650, 654, 678, 748, 762, 786, 822, 834, 860, 894, 906, 940, 942, 978, 1002, 1014, 1038

Offset

1,1

Comments

Perfect numbers (A000396) are a proper subset of this sequence. Weird numbers (A006037) are numbers whose proper divisors sum to more than the number, but no subset sums to the number.

Odd elements are rare: the first few are 8925, 32445, 351351, 442365; there are no more below 100 million. See A065235 for more details.

A065205(a(n)) = 1. - Reinhard Zumkeller, Jan 21 2013

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (terms 1..200 from T. D. Noe, terms 201..5000 from Amiram Eldar)

Example

Proper divisors of 20 are 1, 2, 4, 5 and 10. {1,4,5,10} is the only subset that sums to 20, so 20 is in the sequence.

Mathematica

okQ[n_]:= Module[{d=Most[Divisors[n]]}, SeriesCoefficient[Series[ Product[ 1+x^i, {i, d}], {x, 0, n}], n] == 1]; Select[ Range[ 1100], okQ] (* Harvey P. Dale, Dec 13 2010 *)

Prog

(Haskell)
a064771 n = a064771_list !! (n-1)
a064771_list = map (+ 1) $ elemIndices 1 a065205_list
-- Reinhard Zumkeller, Jan 21 2013

Crossrefs

A005835 gives n such that some subset of S(n) sums to n. Cf. A065205.

Cf. A000396, A006037, A065205, A065235.

Cf. A027751.

Sequence in context: A006039 A180332 A338133 * A006036 A308710 A242341

Adjacent sequences: A064768 A064769 A064770 * A064772 A064773 A064774

Keyword

nonn,nice

Author

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 19 2001

Extensions

More terms from Don Reble, Jud McCranie and Naohiro Nomoto, Oct 22 2001

Status

approved